Quantum Monte Carlo Simulation of an SO(N) Singlet Projector Model on the Pyrochlore Lattice

Over the last decade, the search for deconfined quantum critical points on a variety of models and lattices has revealed possible opportunities for identifying and characterizing phase transitions involving exotic quantum phases, such as valence bond solids and quantum spin liquids. Due to the lattice’s geometric frustration, quantum Monte Carlo (QMC) simulations deployed on the pyrochlore lattice have potential to exhibit such transitions at sufficiently high values of the number of spin colors, N. Thus, we deployed an SO(N)-symmetric singlet-projector model, using a stochastic series expansion QMC simulation, to explore these possibilities. Our primary focus involved using high-performance computing resources to identify the critical value N_c such that, for N>Nc, magnetic order is destroyed. Moreover, we added to our singlet-projection model (J₁ coupling) a second J₂ term, which favors magnetic order, to allow for controlled study of the phase transition as approached from a large value of N. Our characterization of the phase transition (as either first-order or continuous) based on data obtained from large system sizes near the transition point will be presented. Finally, based on these results, potential future directions for this project are briefly discussed.